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Properties

Label 960.3.bn.a
Level $960$
Weight $3$
Character orbit 960.bn
Analytic conductor $26.158$
Analytic rank $0$
Dimension $64$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [960,3,Mod(271,960)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(960, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 1, 0, 0]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("960.271");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 960 = 2^{6} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 960.bn (of order \(4\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(26.1581053786\)
Analytic rank: \(0\)
Dimension: \(64\)
Relative dimension: \(32\) over \(\Q(i)\)
Twist minimal: no (minimal twist has level 240)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 64 q+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 64 q + 64 q^{11} - 32 q^{19} - 256 q^{23} - 64 q^{29} + 192 q^{37} + 192 q^{43} + 448 q^{49} - 96 q^{51} + 320 q^{53} - 128 q^{59} + 32 q^{61} + 64 q^{67} - 96 q^{69} + 512 q^{71} - 448 q^{77} - 576 q^{81} - 160 q^{85} - 576 q^{91} + 192 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Display 100 coefficients 10 coefficients

Embeddings

For each embedding \(\iota_m\) of the coefficient field, the values \(\iota_m(a_n)\) are shown below.

For more information on an embedded modular form you can click on its label.

comment: embeddings in the coefficient field
 
gp: mfembed(f)
 
Label   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
271.1 0 −1.22474 − 1.22474i 0 1.58114 + 1.58114i 0 11.0047 0 3.00000i 0
271.2 0 −1.22474 − 1.22474i 0 1.58114 + 1.58114i 0 9.52201 0 3.00000i 0
271.3 0 −1.22474 − 1.22474i 0 −1.58114 − 1.58114i 0 9.60974 0 3.00000i 0
271.4 0 −1.22474 − 1.22474i 0 −1.58114 − 1.58114i 0 8.42448 0 3.00000i 0
271.5 0 −1.22474 − 1.22474i 0 1.58114 + 1.58114i 0 6.89370 0 3.00000i 0
271.6 0 −1.22474 − 1.22474i 0 −1.58114 − 1.58114i 0 2.50432 0 3.00000i 0
271.7 0 −1.22474 − 1.22474i 0 −1.58114 − 1.58114i 0 2.37589 0 3.00000i 0
271.8 0 −1.22474 − 1.22474i 0 −1.58114 − 1.58114i 0 2.14501 0 3.00000i 0
271.9 0 −1.22474 − 1.22474i 0 1.58114 + 1.58114i 0 −0.712173 0 3.00000i 0
271.10 0 −1.22474 − 1.22474i 0 1.58114 + 1.58114i 0 −0.921374 0 3.00000i 0
271.11 0 −1.22474 − 1.22474i 0 −1.58114 − 1.58114i 0 −6.63610 0 3.00000i 0
271.12 0 −1.22474 − 1.22474i 0 1.58114 + 1.58114i 0 −6.93561 0 3.00000i 0
271.13 0 −1.22474 − 1.22474i 0 1.58114 + 1.58114i 0 −6.96024 0 3.00000i 0
271.14 0 −1.22474 − 1.22474i 0 −1.58114 − 1.58114i 0 −7.82967 0 3.00000i 0
271.15 0 −1.22474 − 1.22474i 0 −1.58114 − 1.58114i 0 −10.5937 0 3.00000i 0
271.16 0 −1.22474 − 1.22474i 0 1.58114 + 1.58114i 0 −11.8910 0 3.00000i 0
271.17 0 1.22474 + 1.22474i 0 1.58114 + 1.58114i 0 12.5907 0 3.00000i 0
271.18 0 1.22474 + 1.22474i 0 −1.58114 − 1.58114i 0 9.39086 0 3.00000i 0
271.19 0 1.22474 + 1.22474i 0 −1.58114 − 1.58114i 0 9.13125 0 3.00000i 0
271.20 0 1.22474 + 1.22474i 0 1.58114 + 1.58114i 0 7.31911 0 3.00000i 0
See all 64 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 271.32
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
16.f odd 4 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 960.3.bn.a 64
4.b odd 2 1 240.3.bn.a ✓ 64
16.e even 4 1 240.3.bn.a ✓ 64
16.f odd 4 1 inner 960.3.bn.a 64
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
240.3.bn.a ✓ 64 4.b odd 2 1
240.3.bn.a ✓ 64 16.e even 4 1
960.3.bn.a 64 1.a even 1 1 trivial
960.3.bn.a 64 16.f odd 4 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(960, [\chi])\).